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# For the circle in the xy-plane, ﬁnd the following. 22( x−1)

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For the circle in the xy-plane, ﬁnd the following. 22( x−1) [#permalink]  24 May 2019, 08:19
Expert's post
For the circle $$( x−1)^2 +(y+1)^2 =20$$ in the xy-plane, ﬁnd the following.

(a) Coordinates of the center

(c) Area

[Reveal] Spoiler: OA
(a) (1,-1) (b) $$\sqrt{20}$$ (c) $$20 \pi$$

Math Review
Question: 20
Page: 245
Difficulty: medium

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Re: For the circle in the xy-plane, ﬁnd the following. 22( x−1) [#permalink]  09 Aug 2019, 11:13
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Expert's post
Carcass wrote:
For the circle $$(x−1)^2 +(y+1)^2 =20$$ in the xy-plane, ﬁnd the following.

(a) Coordinates of the center

(c) Area

[Reveal] Spoiler: OA
(a) (1,-1) (b) $$\sqrt{20}$$ (c) $$20 \pi$$

Math Review
Question: 20
Page: 245
Difficulty: medium

KEY CONCEPTS: The equation $$(x−a)^2 +(y-b)^2 = r^2$$ represents a circle with:
Center (a, b)

GIVEN: $$(x−1)^2 +(y+1)^2=20$$
Rewrite as: $$(x−1)^2 +[y+(-1)]^2 =(\sqrt{20})^2$$

This means....
(a) Coordinates of the center

Answer: $$\sqrt{20}$$ (aka $$2\sqrt{5}$$)

(c) Area
Area of circle = $$\pi r^2 = \pi(\sqrt{20})^2 = 20\pi$$

Cheers,
Brent
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Re: For the circle in the xy-plane, ﬁnd the following. 22( x−1) [#permalink]  09 Aug 2019, 14:20
Thanks! Great stuff!
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Re: For the circle in the xy-plane, ﬁnd the following. 22( x−1) [#permalink]  18 Nov 2019, 22:22
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Carcass wrote:
For the circle $$( x−1)^2 +(y+1)^2 =20$$ in the xy-plane, ﬁnd the following.

(a) Coordinates of the center

(c) Area

[Reveal] Spoiler: OA
(a) (1,-1) (b) $$\sqrt{20}$$ (c) $$20 \pi$$

Math Review
Question: 20
Page: 245
Difficulty: medium

The general equation of a circle is $$(x-a)^2 + (y-b)^2 = r^2$$
where (a,b) is the centre and r is the radius.
Comparing with the values given in the question, we get the a = 1, b = -1 and r^2 = 20.
Centre = (1,-1)
Radius = $$\sqrt{20}$$ = 2$$\sqrt{5}$$
and area = pi*r^2 = 20pi
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Re: For the circle in the xy-plane, ﬁnd the following. 22( x−1)   [#permalink] 18 Nov 2019, 22:22
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